Chapter 9
Computer Simulation of the Process
of Loss of Stability of Composite
Cylindrical Shells Under Combined
Quasi-static and Dynamic Loads
Nikolaii A. Abrosimov, Aleksandr V. Elesin, and Leonid Igumnov
Abstract Based on the applied theory of shells, an energy-consistent resolving
system of equations is constructed, and a complex numerical method is developed
which, within the framework of an explicit variational-difference scheme, makes
it possible to solve both quasi-static and dynamic problems of nonlinear nonaxisymmetric deformation and loss of stability of composite cylindrical shells. The
reliability of the developed method is substantiated by comparing calculation results
with experimental data. The characteristic forms and critical buckling loads of GRP
cylindrical shells as functions of the level of preloading by a quasi-static internal pressure and of the subsequent dynamic loading by an external pressure are analyzed for
various reinforcement patterns in a wide range of loading rate.
Keywords Composite materials · Cylindrical shells · Nonlinear deformation ·
Stability · Numerical methods · quasi-static and dynamic loads
9.1 Introduction
Due to their high strength and rigidity characteristics, composite materials offer
great possibilities for creating rational designs in various areas of modern engineering. When in service, structural elements made from composite materials can
be subjected to combined dynamic and static loads, leading to considerable changes
in form and buckling instability of the elements. To effectively utilize the potentialities of composite materials, comprehensive studies on the dynamic deformation
and buckling instability of structural elements made from materials under combined
quasi-static and dynamic effects are necessary.
The current investigations in this direction are devoted, as a rule, to the analysis of the nonlinear behavior and buckling instability of cylindrical shells made
from traditional isotropic materials (Manevich et al. 1977; Baskakov et al. 1982;
N. A. Abrosimov · A. V. Elesin · L. Igumnov (B)
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russian Federation
e-mail: igumnov@mech.unn.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_9
125
Computer Simulation of the Process
of Loss of Stability of Composite
Cylindrical Shells Under Combined
Quasi-static and Dynamic Loads
Nikolaii A. Abrosimov, Aleksandr V. Elesin, and Leonid Igumnov
Abstract Based on the applied theory of shells, an energy-consistent resolving
system of equations is constructed, and a complex numerical method is developed
which, within the framework of an explicit variational-difference scheme, makes
it possible to solve both quasi-static and dynamic problems of nonlinear nonaxisymmetric deformation and loss of stability of composite cylindrical shells. The
reliability of the developed method is substantiated by comparing calculation results
with experimental data. The characteristic forms and critical buckling loads of GRP
cylindrical shells as functions of the level of preloading by a quasi-static internal pressure and of the subsequent dynamic loading by an external pressure are analyzed for
various reinforcement patterns in a wide range of loading rate.
Keywords Composite materials · Cylindrical shells · Nonlinear deformation ·
Stability · Numerical methods · quasi-static and dynamic loads
9.1 Introduction
Due to their high strength and rigidity characteristics, composite materials offer
great possibilities for creating rational designs in various areas of modern engineering. When in service, structural elements made from composite materials can
be subjected to combined dynamic and static loads, leading to considerable changes
in form and buckling instability of the elements. To effectively utilize the potentialities of composite materials, comprehensive studies on the dynamic deformation
and buckling instability of structural elements made from materials under combined
quasi-static and dynamic effects are necessary.
The current investigations in this direction are devoted, as a rule, to the analysis of the nonlinear behavior and buckling instability of cylindrical shells made
from traditional isotropic materials (Manevich et al. 1977; Baskakov et al. 1982;
N. A. Abrosimov · A. V. Elesin · L. Igumnov (B)
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russian Federation
e-mail: igumnov@mech.unn.ru
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_9
125